Torque tubes and manufacturing methods thereof

ABSTRACT

One aspect of the present disclosure relates to an apparatus comprising a first end fitting. The first end fitting comprises a tube engagement portion. The tube engagement portion comprises an outer coupling surface. The outer coupling surface comprises a first virtual cross-section. The first virtual cross-section comprises a first transverse inflection point. Each point along the first virtual cross-section has a first virtual tangent line coplanar with the first virtual cross-section.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional application claiming priority to U.S.application Ser. No. 14/444,175, entitled “TORQUE TUBES ANDMANUFACTURING METHODS THEREOF,” filed on Jul. 28, 2014, (Docket No.13-1923_BNGCP037US), which is incorporated herein by reference in itsentirety for all purposes.

BACKGROUND

Torque tubes are typically used for transmitting power, e.g., from adrive unit to a driven unit. For example, a vehicle, such as anautomobile, may utilize a torque tube for transferring power, e.g., froma transmission to a differential. In this application, a torque tube maybe referred to as a propeller shaft or a drive shaft. In anotherexample, a torque tube may be used in an aircraft control system fortransmitting torsional forces to control surfaces, such as ailerons andflaps.

A typical torque tube is hollow and has an elongated shape. The torquetube may be made of aluminum or from other suitable materials capable ofwithstanding the torque transferred through the tube. During themanufacturing process, end fittings with outer surfaces having angularridges are inserted into the ends of the torque tube. The ends of thetube are then conformed to (swaged over) the end fittings to formcomplementary geometric features on the inner surface of the tube fortorque tube engaging the angular ridges of the end fittings. Theabove-described couplings prevent slippage of the end fittings withrespect to the torque tube and transfer torsional loads between the endfittings and the tube section.

When a torque tube is conformed to end fittings configured as describedabove, the walls of the tube may become susceptible to cracking. Thesecracks may reduce the expected life of the tube and parts containingcracks should be removed from service.

SUMMARY

Accordingly, apparatus and method, intended to address theabove-identified concerns, would find utility.

One aspect of the present disclosure relates to an apparatus comprisinga first end fitting. The first end fitting comprises a tube engagementportion. The tube engagement portion comprises an outer couplingsurface. The outer coupling surface comprises a first virtualcross-section. The first virtual cross-section comprises a firsttransverse inflection point. Each point along the virtual firstcross-section has a first virtual tangent line coplanar with the firstvirtual cross-section.

One aspect of the present disclosure relates to a vehicle comprising anapparatus. The apparatus comprises a first end fitting comprising a tubeengagement portion. The tube engagement portion comprises an outercoupling surface. All contours of the outer coupling surface are smooth.The outer coupling surface comprises at least one first concavity and atleast one first convexity. The apparatus also comprises a second endfitting and a torque tube. The torque tube comprises a first end and asecond end. The first end of the torque tube is coupled to the first endfitting. The second end of the torque tube is coupled to the second endfitting. The first end of the torque tube comprises an end fittingengagement portion. The end fitting engagement portion comprises aninner coupling surface conformed to the outer coupling surface of thetube engagement portion of the first end fitting. All contours of theinner coupling surface are smooth. The inner coupling surface comprisesat least one second convexity complementary to the at least one firstconcavity of the outer coupling surface of the tube engagement portion.The inner coupling surface comprises at least one second concavitycomplementary to the at least one first convexity of the outer couplingsurface of the tube engagement portion. The vehicle also comprises adrive unit coupled to the first end fitting and a driven unit coupled tothe second end fitting.

One aspect of the present disclosure relates to a method formanufacturing the apparatus. The method comprises installing aprotective sleeve over the end of the torque tube. The method alsocomprises installing a conductive sleeve over the protective sleeve. Themethod also comprises inserting the first end fitting into the end ofthe torque tube. The tube engagement portion of the first end fitting isinserted into the end of the torque tube during this operation. The tubeengagement portion comprises the outer coupling surface. The method alsocomprises electromagnetically forming the end of the torque tube toconform the torque tube to the outer coupling surface of the first endfitting. The method further comprises removing the conductive sleeve andremoving the protective sleeve.

BRIEF DESCRIPTION OF THE DRAWINGS

Having thus described examples of the disclosure in general terms,reference will now be made to the accompanying drawings, which are notnecessarily drawn to scale, and wherein like reference charactersdesignate the same or similar parts throughout the several views, andwherein:

FIG. 1 is a block diagram of an apparatus, which may be a part of avehicle and which comprises an end fitting and, optionally, a torquetube, according to one aspect of the present disclosure;

FIG. 2A is a schematic perspective view of the apparatus of FIG. 1 priorto inserting the end fitting into the torque tube, according to oneaspect of the present disclosure;

FIG. 2B is a schematic perspective view of the apparatus of FIG. 1 priorto inserting the end fitting, which includes flats, into the torquetube, according to one aspect of the present disclosure;

FIG. 3A is a schematic cross-sectional view of an end fitting of FIGS. 1and 2A, according to one aspect of the present disclosure;

FIG. 3B is a schematic cross-sectional view of an end fitting of FIGS. 1and 2B including flats, according to one aspect of the presentdisclosure;

FIG. 4A is a schematic longitudinal sectional view of an end fitting ofFIGS. 1 and 2A, according to one aspect of the present disclosure;

FIG. 4B is a schematic longitudinal sectional view of an end fitting ofFIGS. 1 and 2B including flats, according to one aspect of the presentdisclosure;

FIG. 4C is a schematic detail view of a portion of the end fitting ofFIG. 1 and FIG. 4B including flats, according to one aspect of thepresent disclosure;

FIG. 5 is a schematic cross-sectional view of the apparatus of FIG. 1prior to forming the torque tube to conform to the end fitting,according to one aspect of the present disclosure;

FIG. 6A is a schematic perspective view of the apparatus of FIG. 1 afterforming the torque tube to conform to the end fitting, according to oneaspect of the present disclosure;

FIG. 6B is a schematic perspective view of the apparatus of FIG. 1including flats after forming the torque tube to conform to the endfitting, according to one aspect of the present disclosure;

FIG. 7A is a schematic cross-sectional view of the apparatus of FIG. 1after conforming the torque tube to the end fitting, according to oneaspect of the present disclosure;

FIG. 7B is a schematic cross-sectional view of the apparatus of FIG. 1including flats after conforming the torque tube to the end fitting,according to one aspect of the present disclosure;

FIG. 8 is a schematic longitudinal sectional view of the apparatus ofFIG. 1 after conforming the torque tube to the end fitting, according toone aspect of the present disclosure;

FIG. 9 is a block diagram of a method of manufacturing the apparatus ofFIG. 1, according to one aspect of the present disclosure;

FIGS. 10-14 are schematic perspective views of the apparatus of FIG. 1at different stages of its manufacturing, according to one or moreaspects of the present disclosure;

FIG. 15 is a block diagram of aircraft production and servicemethodology;

FIG. 16 is a schematic illustration of an aircraft.

In FIG. 1, above, solid lines, if any, connecting various elementsand/or components may represent mechanical, electrical, fluid, optical,electromagnetic and other couplings and/or combinations thereof. As usedherein, “coupled” means associated directly as well as indirectly. Forexample, a member A may be directly associated with a member B, or maybe indirectly associated therewith, e.g., via another member C. It willbe understood that not all relationships between the various disclosedelements are necessarily represented. Accordingly, couplings other thanthose depicted in the block diagrams may also exist. Dashed lines, ifany, connecting the various elements and/or components representcouplings similar in function and purpose to those represented by solidlines; however, couplings represented by the dashed lines may either beselectively provided or may relate to alternative or optional aspects ofthe present disclosure. Likewise, elements and/or components, if any,represented with dashed lines, indicate alternative or optional aspectsof the present disclosure. Environmental elements, if any, arerepresented with dotted lines. Virtual (imaginary) elements may also beshown for clarity. Those skilled in the art will appreciate that some ofthe features illustrated in FIG. 1 may be combined in various wayswithout the need to include other features described in FIG. 1, otherdrawing figures, and/or the accompanying disclosure, even though suchcombination or combinations are not explicitly illustrated herein.Similarly, additional features not limited to the examples presented,may be combined with some or all of the features shown and describedherein.

In FIGS. 9 and 15, referred to above, the blocks may representoperations and/or portions thereof and lines connecting the variousblocks do not imply any particular order or dependency of the operationsor portions thereof. FIGS. 9 and 15 and the accompanying disclosuredescribing the operations of the method(s) set forth herein should notbe interpreted as necessarily determining a sequence in which theoperations are to be performed. Rather, although one illustrative orderis indicated, it is to be understood that the sequence of the operationsmay be modified when appropriate. Accordingly, certain operations may beperformed in a different order or simultaneously. Additionally, thoseskilled in the art will appreciate that not all operations describedneed be performed.

DETAILED DESCRIPTION

In the following description, numerous specific details are set forth toprovide a thorough understanding of the disclosed concepts, which may bepracticed without some or all of these particulars. In other instances,details of known devices and/or processes have been omitted to avoidunnecessarily obscuring the disclosure. While some concepts will bedescribed in conjunction with specific aspects and examples, it will beunderstood that these aspects and examples are not intended to belimiting.

Reference herein to “one aspect” or “one example” means that one or morefeature, structure, or characteristic described in connection with theaspect or example is included in at least one implementation. The phrase“one aspect” or “one example” in various places in the specification mayor may not be referring to the same aspect or example.

Unless otherwise indicated, the terms “first,” “second,” etc. are usedherein merely as labels, and are not intended to impose ordinal,positional, or hierarchical requirements on the items to which theseterms refer. Moreover, reference to, e.g., a “second” item does notrequire or preclude the existence of, e.g., a “first” or lower-numbereditem, and/or, e.g., a “third” or higher-numbered item.

As used herein, any means-plus-function clause is to be interpretedunder 35 U.S.C. 112(f), unless otherwise explicitly stated. It should benoted that examples provided herein of any structure, material, or actin support of any means-plus-function clause, and equivalents thereof,may be utilized individually or in combination. Thus, while variousstructures, materials, or acts may be described in connection with ameans-plus-function clause, any combination thereof or of theirequivalents is contemplated in support of such means-plus-functionclause.

Referring generally to FIGS. 1-2B, and with particular reference toFIGS. 3A-3B, aspect 1 of the present disclosure relates to apparatus 100comprising first end fitting 110 a. First end fitting 110 a comprisestube engagement portion 112. Tube engagement portion 112 comprises outercoupling surface 114. Outer coupling surface 114 comprises first virtualcross-section 118 (shown, e.g., in FIGS. 3A and 3B). First virtualcross-section 118 comprises first transverse inflection point 119. Eachpoint along first virtual cross-section 118 has first virtual tangentline 120 coplanar with first virtual cross-section 118. As used herein,“virtual” means having the attributes of a feature without possessingits physical form. In some aspects, apparatus 100 includes othercomponents, such as torque tube 130, further described below, and, inother aspects, apparatus 100 includes an additional end fitting, such assecond end fitting 110 b (shown, e.g., in FIG. 1), which is similar oridentical to first end fitting 110 a. In addition to tube engagementportion 112, in one aspect, first end fitting 110 a includes connectorportion 111 further describe below.

As shown, e.g., in FIGS. 3A and 3B, which illustrate first virtualcross-section 118, the presence of first virtual tangent line 120 ateach point along first virtual cross-section 118 indicates that none ofthese points is a vertex of a corner. As used herein, a corner isconsidered to have a vertex when the corner radius is less than about0.125 inches. This value may be used for torque tube 130 having anoutside diameter of between about 1 inch and 2 inches or, morespecifically, between about 1.25 inches and 1.5 inches. In general, aratio of the outside diameter to the corner radius may be between about5 and 20 such as about 10. In other words, each position of firstvirtual cross-section 118 has a curvature of at least about 0.125inches. It should be noted that only virtual tangent lines that arecoplanar with first virtual cross-section 118 are indicative of thisfeature. In other words, the shape of outer coupling surface 114 isanalyzed within the plane defined by first virtual cross-section 118.Outer coupling surface 114 is represented by a smooth curve at firstvirtual cross-section 118. As such, outer coupling surface 114 does nothave edges intersecting at least first virtual cross-section 118 thatotherwise may cause cracking or some other damage to torque tube 130,particularly when torque tube 130 is electromagnetically formed overfirst end fitting 110 a. It should be noted that during electromagneticforming, inner coupling surface 134 of end fitting portion 132 of torquetube 130 conforms to outer coupling surface 114 of tube engagementportion 112 of first end fitting 110 a. Therefore, the absence of sharpedges on outer coupling surface 114, as evident by the absence of thecorner vertices in first virtual cross-section 118, reduces the risk ofstress cracking in end fitting engagement portion 132.

The presence of first transverse inflection point 119 indicates thatfirst virtual cross-section 118 of outer coupling surface 114 includesboth convex and concave portions. For purposes of this disclosure, aninflection point is defined as a transition point between a concaveportion and a convex portion, a concave portion and a flat portion, or aconvex portion and a flat portion of a line representing first virtualcross-section 118. For purposes of this disclosure, first virtualcross-section 118 is perpendicular to the direction of the torque Ttransferred by apparatus 100, e.g., from drive unit 102 to driven unit103 (FIG. 1). In the example shown in FIGS. 6A and 6B, the torquedirection is substantially coaxial to the center axis of torque tube130. As such, first virtual cross-section 118 of tube engagement portion112 is distinguishable from other shapes without corner vertexes (asdefined above), such as ovals or circles, having only convex portions.

In some aspects, first virtual cross-section 118 includes multiple firsttransverse inflection points 119. As an example, first virtualcross-section 118 includes at least two first transverse inflectionpoints 119 wherein, first transverse inflection point 119 separatesfirst concavity 124 from first convexity 126. For example, FIG. 3Aillustrates first virtual cross-section 118 having twelve firsttransverse inflection points 119 separating six first concavities 124from six first convexities 126 forming first virtual cross-section 118,according to one aspect of the disclosure. The number of firsttransverse inflection points 119 depends on the number of firstconcavities 124 and first convexities 126, which, in turn depends, atleast in part, on the overall size (e.g., an outer diameter) of tubeengagement portion 112, wall thickness of torque tube 130, material oftorque tube 130, depth and/or curvature of first concavities 124 andfirst convexities 126, and/or other factors.

In some aspects, first transverse inflection point 119 may be positionedbetween first flat 125 and one of first concavity 124 and firstconvexity 126. This type of transverse inflection points should bedistinguished from a transverse inflection point formed by a concavityand an adjacent convexity. For example, FIG. 3B illustrates firstvirtual cross-section 118 having twenty four first transverse inflectionpoints 119 separating six first concavities 124 from twelve first flats125 and also separating twelve first flats 125 from six firstconvexities 126. Specifically, each of twelve first flats 125 separate apair of first concavity 124 and first convexity 126. Each end of eachfirst flat 125 is defined by first transverse inflection point 119. Inthis example, each first concavity 124 is disposed between two firstflats 125 and each first convexity 126 is disposed between two firstflats 125. First transverse inflection point 119 define transitions fromfirst flats 125 to first convexities 126 and first flats 125 to firstconcavities 124.

Referring, e.g., to FIGS. 1, 6A, 6B, 7A and 7B, aspect 2 of the presentdisclosure, which includes at least a portion of the subject matter ofaspect 1 and may also include at least a portion of the subject matterof any other aspect or aspects disclosed herein, apparatus 100 comprisestorque tube 130 coupled to first end fitting 110 a. Torque tube 130comprises end fitting engagement portion 132 conformed to tubeengagement portion 112 of first end fitting 110 a. End fittingengagement portion 132 comprises inner coupling surface 134. Innercoupling surface 134 comprises second virtual cross-section 138 (shown,e.g., in FIGS. 7A and 7B) coplanar with and complementary to firstvirtual cross-section 118 of outer coupling surface 114 of first endfitting 110 a. Second virtual cross-section 138 comprises secondtransverse inflection point 142. Each point along second virtualcross-section 138 has second virtual tangent line 143 coplanar withsecond virtual cross-section 138. The presence of second virtual tangentline 143 at each point along second virtual cross-section 138 indicatesthat none of these points is a vertex of a corner. Second virtualcross-section 138 or, more specifically, a line representing secondvirtual cross-section 138, is a smooth curve. The shape of secondvirtual cross-section 138 is complementary to or, more specifically,conforms to the shape of first virtual cross-section 118. As notedabove, end fitting engagement portion 132 of torque tube 130 conforms totube engagement portion 112 of first end fitting 110 a such that innercoupling surface 134 of end fitting engagement portion 132 iscomplementary to and conforms to outer coupling surface 114 of tubeengagement portion 112. In one aspect, once apparatus 100 is assembled,inner coupling surface 134 substantially contacts outer coupling surface114, providing engagement of first end fitting 110 a and torque tube 130and allowing torque transfer between first end fitting 110 a and torquetube 130.

As further described below, end fitting engagement portion 132 of torquetube 130 is swaged onto or, more specifically, electromagneticallyformed over tube engagement portion 112 of first end fitting 110 a. Inaddition to contacting inner coupling surface 134, in one aspect, outercoupling surface 114 defines the shape of inner coupling surface 134. Inone aspect, absence of corner vertexes along first virtual cross-section118 results in a similar absence of corners vertexes along secondvirtual cross-section 138.

Second transverse inflection point 142 indicates that, similar to firstvirtual cross-section 118, second virtual cross-section 138 includesboth convex and concave portions. In one aspect, second virtualcross-section 138 includes a plurality of second transverse inflectionpoints 142. The number and location of second transverse inflectionpoints 142 on second virtual cross-section 138 generally corresponds tothe number and location of first transverse inflection points 119 onfirst virtual cross-section 118. The shapes of first virtualcross-section 118 and second virtual cross-section 138 conform to eachother providing tight fit between tube engagement portion 112 of firstend fitting 110 a and end fitting engagement portion 132 of torque tube130.

Referring e.g. to FIGS. 1, 7A and 7B, in aspect 3 of the presentdisclosure, which includes at least a portion of the subject matter ofaspect 2 and may also include at least a portion of the subject matterof any other aspect or aspects disclosed herein, end fitting engagementportion 132 of torque tube 130 comprises outer surface 154. Outersurface 154 comprises third virtual cross-section 156 coplanar withsecond virtual cross-section 138 of inner coupling surface 134. Thirdvirtual cross-section 156 comprises third transverse inflection point158. Each point along third virtual cross-section 156 has third virtualtangent line 160 coplanar with third virtual cross-section 156. Thepresence of third virtual tangent line 160 at each point along thirdvirtual cross-section 156 and the fact that each third virtual tangentline 160 is coplanar with third virtual cross-section 156 indicates thatneither one of the points along third virtual cross-section 156 is acorner. Third virtual cross-section 156 is a smooth curve or, morespecifically, a curve representing outer surface 154 at third virtualcross-section 156 is smooth and does not have corners. In fact, theseparation between third virtual cross-section 156 corresponding toouter surface 154 and second virtual cross-section 138 corresponding toinner coupling surface 134 is set by the wall thickness of torque tube130 at second virtual cross-section 138 and third virtual cross-section156. In some example, the wall thickness is substantially uniform (e.g.,varies by less than 25% or even by less than 10%) along third virtualcross-section 156 and second virtual cross-section 138. Changing (e.g.,reducing) the wall thickness during forming of end fitting engagementportion 132 is generally undesirable in order to maintain structuralintegrity of end fitting engagement portion 132.

Referring e.g. to FIG. 1, in aspect 4 of the present disclosure, whichincludes at least a portion of the subject matter of any of aspects 2-3and may also include at least a portion of the subject matter of anyother aspect or aspects disclosed herein, torque tube 130 comprisestitanium. Titanium has a high tensile strength to density ratio, highcorrosion resistance, fatigue resistance, high crack resistance, andability to withstand moderately high temperatures without creeping,which makes titanium and, more specifically, torque tube 130 comprisingtitanium particularly suitable for various applications, such asaircraft applications. Furthermore, fatigue resistance and high crackresistance make of titanium allows forming torque tube 130 into aparticular shape over first end fitting 110 a as, for example, shown inFIGS. 7A and 7B. This shape defined by third virtual cross-section 156and second virtual cross-section 138 provides engagement between torquetube 130 and first end fitting 110 a and allows torque transfer. Theshape needs to be retained during operation of apparatus 100. In someembodiments, torque tube 130 comprises as an alloy of titanium. In oneaspect, one or more other components of this alloy are aluminum,zirconium, nickel, vanadium, and various combinations thereof. Aparticular example is a Ti64 alloy which includes 6% aluminum, 4%vanadium, 0.25% (maximum) iron, 0.2% (maximum) oxygen, and the remaindertitanium. Mechanical properties of titanium allow forming much thinnertorque tube 130 than when aluminum is used, for example, resulting inweight savings. In general, other materials such as steel, copper, andaluminum, can be used to torque tube 130. Corrosion resistance steel,such as stainless steel, can be used for first end fitting 110 a.

Referring e.g. to FIGS. 1, 7A and 7B, in aspect 5 of the presentdisclosure, which includes at least a portion of the subject matter ofany of aspects 2-4 and may also include at least a portion of thesubject matter of any other aspect or aspects disclosed herein, torquetube 130 has a wall thickness between about 0.02 and about 0.08 inchesor, more specifically, between about 0.04 and about 0.06 inches. In someaspects, smaller wall thicknesses are not be suitable for torquetransfer applications since torque tube 130 can collapse when anexcessive torque is applied to torque tube 130. As such, the torquetransfer rating of torque tube 130 is one factor in selecting the wallthickness of the torque tube. At the same time, torque tube 130 havinglarger thicknesses may be too heavy for some applications (e.g.,aircraft) and/or too difficult to form over first end fitting 110 a. Thewall thickness values presented above may be used for torque tube 130having an outside diameter of between 1 inch and 1.5 inches. In additionthe outside diameter, another parameter that may influence the wallthickness selection is the minimum corner radius described above toreduce the risk of cracking during forming as well as torque transfer.For purposes of this disclosure, the values of the wall thickness referto the average value of the wall thickness along second virtualcross-section 138 and third virtual cross-section 156 as well as alongsecond virtual longitudinal section 144 and third virtual longitudinalsection 162.

Referring e.g. to FIGS. 1, 7A and 7B, in one example of the presentdisclosure, which may include at least a portion of the subject matterof any other aspect(s) and/or example(s) disclosed herein, torque tube130 has an outside diameter between about 0.50 inches and about 4.00inches or, more specifically, between about 1.0 inch and about 2.0inches. For purposes of this disclosure, the values of the outsidediameter refer to the outside diameter of a portion of torque tube 130that is not formed or, more specifically, is not a part of end fittingengagement portion 132. In general, the outside diameter of torque tube130 depends on the wall thickness as described above. In some examples(when torque tube 130 snugly fits over first end fitting 110 a prior toforming and when end fitting engagement portion 132 comprises an evennumber of second concavities 170 uniformly spaced apart), the distancebetween the tips of two second concavities 170 disposed diametricallyopposite from each other along the second virtual cross-section 138 isthe same as the outside diameter.

Referring e.g. to FIGS. 1, 2A, 2B, 4A and 4B in aspect 6 of the presentdisclosure, which includes at least a portion of the subject matter ofany of aspects 1-5 and may also include at least a portion of thesubject matter of any other aspect or aspects disclosed herein, firstend fitting 110 a comprises connector portion 111 adjacent tubeengagement portion 112. Connector portion 111 comprises means 113 forconnecting apparatus 100 to one of drive unit 102 or driven unit 103.While FIG. 1 illustrates that means 113 is connected to drive unit 102,one having ordinary skills in the art would understand that means 113can be connected to either one of drive unit 102 or driven unit 103. Inone example, means 113 is an opening for receiving a pin such that aportion of the pin extends into drive unit 102 or driven unit 103. Inanother aspect, means 113 is a spline having ridges or teeth onconnector portion 111 that mesh with grooves of drive unit 102 or drivenunit 103. Examples of spline types includes parallel key splines,involute splines, crowned splines, serrations, helical splines, and ballsplines.

Referring e.g. to FIGS. 1 and 4A-4B, in aspect 7 of the presentdisclosure, which includes at least a portion of the subject matter ofany of aspects 1-6 and may also include at least a portion of thesubject matter of any other aspect or aspects disclosed herein, outercoupling surface 114 of tube engagement portion 112 of first end fitting110 a comprises first virtual longitudinal section 121. First virtuallongitudinal section 121 comprises first longitudinal inflection point122. Each point along first virtual longitudinal section 121 has fourthvirtual tangent line 123 coplanar with first virtual longitudinalsection 121. The presence of fourth virtual tangent line 123 at eachpoint along first virtual longitudinal section 121 indicates thatneither one of these points is a vertex of a corner. First virtuallongitudinal section 121 of outer coupling surface 114 is smooth curveand does not have vertices of corners. As such, outer coupling surface114 does not have edges intersecting at least first virtual longitudinalsection 121 that otherwise may cause cracking of or may damage torquetube 130, particularly, when torque tube 130 is formed over first endfitting 110 a. It should be noted that other portions of first endfitting 110 a that do not include outer coupling surface and that arenot used to form torque tube 130, such as connector portion 111, haveone or more corner vertices in some aspects. Specifically, in oneaspect, first end fitting 110 a includes at least one corner vertexoutside of the outer coupling surface 114. However, these corners do nothave impact forming of torque tube 130. First longitudinal inflectionpoint 122 indicates that first virtual longitudinal section 121 includesboth convex and concave portions. As shown in FIGS. 4A-4B, first virtuallongitudinal section 121 includes two first convexities 126 and twofirst concavities 124.

Referring generally e.g. to FIGS. 1, 2A, 2B, 6A, 6B, 7A, 7B, and 8 and,more specifically, to FIG. 8, in aspect 8 of the present disclosure,which includes at least a portion of the subject matter of aspect 7 andmay also include at least a portion of the subject matter of any otheraspect or aspects disclosed herein, apparatus 100 comprises torque tube130 coupled to first end fitting 110 a. Torque tube 130 comprises endfitting engagement portion 132 conformed to tube engagement portion 112of first end fitting 110 a. End fitting engagement portion 132 comprisesinner coupling surface 134. Inner coupling surface 134 comprises secondvirtual longitudinal section 144 coplanar with and complementary tofirst virtual longitudinal section 121 of outer coupling surface 114 oftube engagement portion 112. Second virtual longitudinal section 144comprises second longitudinal inflection point 145. Each point alongsecond virtual longitudinal section 144 has fifth virtual tangent line146 coplanar with second virtual longitudinal section 144. As shown inFIG. 8, the presence of fifth virtual tangent line 146 at each pointalong second virtual longitudinal section 144 indicates that neither oneof these points is a vertex of a corner. Second virtual longitudinalsection 144 is a smooth curve. As such, inner coupling surface 134 doesnot have edges passing though second virtual longitudinal section 144that otherwise may cause cracking or, more generally, may damage torquetube 130. Second longitudinal inflection point 145 indicates that secondvirtual longitudinal section 144 includes both convex and concaveportions. As shown in FIG. 8, second virtual longitudinal section 144includes two second convexities 174 and two second concavities 170.Furthermore, in one aspect, inner coupling surface 134 of tubeengagement portion 112 has the same shape and generally conforms toouter coupling surface 114 of tube engagement portion 112 of first endfitting 110 a. In fact, as further described below, tube engagementportion 112 may serve as a forming template during electromagneticforming of tube engagement portion 112. During this operation, tubeengagement portion 112 is deformed toward outer coupling surface 114 oftube engagement portion 112 until inner coupling surface 134 of tubeengagement portion 112 conforms to outer coupling surface 114 of tubeengagement portion 112.

Referring generally e.g. to FIGS. 1, 2A, 2B, 6A, 6B, 7A, 7B, and 8 and,more specifically, to FIG. 8, in aspect 9 of the present disclosure,which includes at least a portion of the subject matter of aspect 8 andmay also include at least a portion of the subject matter of any otheraspect or aspects disclosed herein, end fitting engagement portion 132comprises outer surface 154. Outer surface 154 comprises third virtuallongitudinal section 162 coplanar with second virtual longitudinalsection 144. Third virtual longitudinal section 162 comprises thirdlongitudinal inflection point 164. Each point along third virtuallongitudinal section 162 has sixth virtual tangent line 166 coplanarwith third virtual longitudinal section 162. It should be noted thatFIG. 8 illustrates both second virtual longitudinal section 144 andthird virtual longitudinal section 162 of torque tube 130. Secondvirtual longitudinal section 144 is described above with reference toinner coupling surface 134 and its features. Third virtual longitudinalsection 162 will now be described with reference to outer surface 154.The correspondence of second virtual longitudinal section 144 and thirdvirtual longitudinal section 162 comes from the fact that inner couplingsurface 134 and outer surface 154 and only separated by the wallthickness of torque tube 130.

As shown in FIG. 8, the presence of sixth virtual tangent line 166 ateach point along third virtual longitudinal section 162 indicates thatneither one of these points is a corner vertex. A line corresponding toouter surface 154 in third virtual longitudinal section 162 is a smoothcurve. As such, outer surface 154 does not have edges passing throughthird virtual longitudinal section 162 that otherwise may cause crackingor, more generally, may damage torque tube 130. Third longitudinalinflection point 164 indicates that third virtual longitudinal section162 includes both convex and concave portions. As shown in FIG. 8, thirdvirtual longitudinal section 162 includes two third convexities 184 andtwo third concavities 180.

Referring generally to FIGS. 2A-8, and with particular reference to FIG.1, aspect 10 of the present disclosure relates to vehicle 104 comprisingapparatus 100. Apparatus 100 comprises first end fitting 110 acomprising tube engagement portion 112. Tube engagement portion 112comprises outer coupling surface 114. All contours of outer couplingsurface 114 are smooth. Outer coupling surface 114 comprises at leastone first concavity 124 and at least one first convexity 126. Apparatus100 also comprises second end fitting 110 b and torque tube 130comprising first end 131 a and second end 131 b. First end 131 a oftorque tube 130 is coupled to first end fitting 110 a. Second end 131 bof torque tube 130 is coupled to second end fitting 110 b. First end 131a of torque tube 130 comprises end fitting engagement portion 132. Endfitting engagement portion 132 comprises inner coupling surface 134conformed to outer coupling surface 114 of tube engagement portion 112of first end fitting 110 a. All contours of inner coupling surface 134are smooth. Inner coupling surface 134 comprises at least one secondconvexity 174 complementary to at least one first concavity 124 of outercoupling surface 114 of tube engagement portion 112. Inner couplingsurface 134 comprises at least one second concavity 170 complementary toat least one first convexity 126 of outer coupling surface 114 of tubeengagement portion 112. Vehicle 104 also comprises drive unit 102coupled to first end fitting 110 a and driven unit 103 coupled to secondend fitting 110 b. In one aspect, vehicle 104 is an aircraft or anyother type of vehicles that use torque tube 130 to transfer torque fromdrive unit 102 to driven unit 103. More specifically, drive unit 102 iscoupled to first end fitting 110 a, which is coupled to first end 131 aof torque tube 130. Driven unit 103 is coupled to second end fitting 110b, which is coupled to second end 131 b of torque tube 130. In someexamples, second end fitting 110 b is the same as first end fitting 110a.

Outer coupling surface 114 of tube engagement portion 112 is shown inFIGS. 3A-3B and 4A-4B. Specifically, first concavity 124 and firstconvexity 126 are shown in two different sectional views, i.e., as apart of first virtual cross-section 118 in FIGS. 3A-3B and as a part offirst virtual longitudinal section 121 in FIGS. 4A-4B. In both of thesefigures, first concavity 124 and first convexity 126 are represented bysmooth curves that do not have any corner vertices. This aspect isdescribed above with respect to first virtual tangent lines 120 andfourth virtual tangent lines 123. Furthermore, this aspect demonstrates,at least in part, that all contours of outer coupling surface 114 aresmooth.

Inner coupling surface 134 of torque tube 130 is shown in FIGS. 7A, 7B,and 8. Specifically, second concavity 170 and second convexity 174 areshown in two different sectional views, i.e., as a part of first virtualcross-section 138 in FIGS. 7A and 7B and as a part of second virtuallongitudinal section 144 in FIG. 8. In both of these figures, secondconcavity 170 and second convexity 174 are represented by smooth curvesthat do not have any corner vertices. This aspect is described abovewith respect to second virtual tangent lines 143 and fifth virtualtangent lines 146. Furthermore, this aspect demonstrates, at least inpart, that all contours of inner coupling surface 134 are smooth.

Referring e.g. to FIGS. 1, 7A, 7B, and 8, in aspect 11 of the presentdisclosure, which includes at least a portion of the subject matter ofaspect 10 and may also include at least a portion of the subject matterof any other aspect or aspects disclosed herein, end fitting engagementportion 132 of torque tube 130 comprises outer surface 154. Outersurface 154 comprises at least one third concavity 180 and at least onethird convexity 184. All contours of outer surface 154 are smooth. Outersurface 154 of torque tube 130 is shown in FIGS. 7A, 7B, and 8.Specifically, third concavity 180 and third convexity 184 are shown intwo different sectional views, i.e., as a part of third virtualcross-section 156 in FIGS. 7A and 7B and as a part of third virtuallongitudinal section 162 in FIG. 8. In both of these figures, thirdconcavity 180 and third convexity 184 are represented by smooth curvesthat do not have any corner vertices. This aspect is described abovewith respect to third virtual tangent lines 160 and sixth virtualtangent lines 166. Furthermore, this aspect demonstrates, at least inpart, that all contours of outer surface 154 are smooth.

Referring e.g. to FIG. 1 and particularly to FIG. 7B, in aspect 12 ofthe disclosure, which includes at least a portion of the subject matterof aspect 11 and may additionally include at least a portion of thesubject matter of any other aspect or aspects disclosed herein, innercoupling surface 134 comprises at least one second flat 172. One or moresecond flats 172 may be complimentary to one or more first flats 125 ofouter coupling surface 114 of tube engagement portion 112 of first endfitting 110 a. In one aspect, the number of second flats 172 is the sameas the number of first flats 125. Alternatively, the number of secondflats 172 is different than the number of first flats 125. For example,inner coupling surface 134 may not fully conform to outer couplingsurface 114 such that one or more portions of inner coupling surface 134may not contact outer coupling surface 114. In some embodiments, theseportions may include one or more second flats 172. Second flat 172 ispositioned between two second transverse inflection points 142, betweentwo second longitudinal inflection points 145, or both sets of points.One end of second flat 172 (e.g., second transverse inflection point 142and/or second longitudinal inflection points 145) may be also an end ofsecond concavity 170. The other end of second flat 172 (e.g., secondtransverse inflection point 142 and/or second longitudinal inflectionpoints 145) may be also an end of second convexity 174. As such, secondflat 172 may be disposed between second concavity 170 and secondconvexity 174. In some aspects, second flat 172 may be disposed betweentwo second concavities 170 or between two second convexities 174.

Referring e.g. to FIGS. 1, 7A, 7B, and 8, in aspect 13 of the presentdisclosure, which includes at least a portion of the subject matter ofaspect 11 and may also include at least a portion of the subject matterof any other aspect or aspects disclosed herein, at least one thirdconcavity 180 comprises a smallest radius of curvature of between about0.125 inches and about 0.5 inches for first end fitting 110 a having anoutside diameter of between 1 inch and 4 inches. In general, the radiusof curvature is scalable with the outside diameter and the ratio of theoutside diameter to the radius of curvature of first end fitting 110 amay be between about 1 and 20 or, more specifically, between about 4 and15, such as about 8.

Referring e.g. to FIGS. 1 and 2B and particularly to FIG. 3B, in aspect14 of the present disclosure, which includes at least a portion of thesubject matter of any of aspects 10-13 and may also include at least aportion of the subject matter of any of other aspect or aspectsdisclosed herein, outer coupling surface 114 of tube engagement portion112 of first end fitting 110 a comprises at least one first flat 125.Each first flat 125 is positioned between two first transverseinflection points 119, between two first longitudinal inflection points122, or both sets of points. One end of first flat 125 (e.g., firsttransverse inflection point 119 and/or first longitudinal inflectionpoints 122) may be also an end of first concavity 124. The other end(e.g., first transverse inflection point 119 and/or first longitudinalinflection points 122) may be formed also an end of first convexity 126.As such, first flat 125 may be disposed between first concavity 124 andfirst convexity 126 as shown in FIG. 3B. Specifically, FIG. 3Billustrates twelve first flats 125 separating six first concavities 124and six first convexities 126. In some aspects, first flat 125 may bedisposed between two first concavities 124 or between two firstconvexities 126. First flat 125 may be a part of first virtualcross-section 118 (as shown in FIG. 3B), first virtual longitudinalsection 118 (as shown in FIGS. 4B and 4C), or both.

Referring e.g. to FIGS. 1 and particularly to FIGS. 6B and 7B in aspect15 of the present disclosure, which includes at least a portion of thesubject matter of any of aspects 10-14 and may also include at least aportion of the subject matter of any other aspect or aspects disclosedherein, outer surface 154 of end fitting engagement portion 132 oftorque tube 130 comprises at least one third flat 182. One or more thirdflats 182 may be complimentary to one or more first flats 125 of outercoupling surface 114 of tube engagement portion 112 of first end fitting110 a. In one aspect, the number of third flats 182 is the same as thenumber of first flats 125. Alternatively, the number of third flats 182is different than the number of first flats 125. For example, innercoupling surface 134 may not fully conform to outer coupling surface 114such that one or more portions of inner coupling surface 134 may notcontact outer coupling surface 114. In some embodiments, these portionsmay include one or more third flats 182. Furthermore, in some aspect,end fitting engagement portion 132 has substantially uniform wallthickness and each of third flats 182 is complimentary to one of secondflats 172.

Third flat 182 is positioned between two third transverse inflectionpoints 158, between two third longitudinal inflection points 164, orboth sets of points. One end of third flat 182 (e.g., third transverseinflection point 158 and/or third longitudinal inflection points 164)may be also an end of third concavity 180. The other end of third flat182 (e.g., third transverse inflection point 158 and/or thirdlongitudinal inflection points 164) may be also an end of thirdconvexity 184. As such, third flat 182 may be disposed between thirdconcavity 180 and third convexity 184. In some aspects, third flat 182may be disposed between two third concavities 180 or between two thirdconvexities 184.

Referring generally to FIGS. 10-14 and particularly to FIG. 9, aspect 16of the present disclosure relates to method 900 for manufacturingapparatus 100. Method 900 comprises installing protective sleeve 1030over first end 131 a of torque tube 130 (block 904) as shown, forexample, in FIG. 10. Method 900 also comprises installing conductivesleeve 1130 over protective sleeve 1030 (block 906), as shown, forexample, in FIG. 11. Method 900 also comprises inserting first endfitting 110 a into end 131 a of torque tube 130 (block 908), as shown,for example, in FIG. 12. Tube engagement portion 112 of first endfitting 110 a is inserted into end 131 a of torque tube 130 during thisoperation. Tube engagement portion 112 comprises outer coupling surface114. Method 900 also comprises electromagnetically forming first end 131a of torque tube 130 to conform torque tube 130 to outer couplingsurface 114 of first end fitting 110 a (block 910), as shown, forexample, in FIG. 13. Method 900 further comprises removing conductivesleeve 1130 (block 912) and removing protective sleeve 1030 (block 914),as shown, for example, in FIG. 14. During electromagnetic forming 910, ahigh intensity changing magnetic field is applied to induce acirculating electrical current in first end 131 a of torque tube 130.The induced current creates a new magnetic field around first end 131 a,and this new magnetic field repels the applied magnetic field causingdeformation of first end 131 a. Specifically, first end 131 a havingprotective sleeve 1030 and conductive sleeve 1130 installed over itsouter surface 154 and first end fitting 110 a inserted into first end131 a, is placed in proximity to a heavily constructed coil of wire,which may be referred to as a work coil. A large pulse of current isforced through the work coil by rapidly discharging a high voltagecapacitor bank using an ignitron or a spark gap as a switch. Thispulsing creates a rapidly oscillating strong electromagnetic fieldaround the work coil that significantly exceeds the yield strength ofthe material of torque tube 130. As a result, torque tube 130 isdeformed or, more specifically, forced against outer coupling surface114 of first end fitting 110 a until torque tube 130 conforms to outercoupling surface 114.

Referring e.g. to FIGS. 1, 10, and 11, in aspect 17 of the presentdisclosure, which includes at least a portion of the subject matteraspect 16 and may also include at least a portion of the subject matterof any other aspect or aspects disclosed herein, protective sleeve 1030comprises plastic. Conductive sleeve 1130 comprises copper. Copper maybe used when torque tube 130 is made from titanium or any other materialhaving a relative high resistivity (e.g., a resistivity of greater than1×10⁻⁶ Ohm-cm) in comparison, for example, to aluminum. For moreconductive materials (e.g., a resistivity of less than 1×10⁻⁶ Ohm-cm),conductive sleeve 1130 may comprise aluminum. Referring e.g. to FIGS. 1,5, 9, and 12, in aspect 18 of the present disclosure, which includes atleast a portion of the subject matter of any of aspects 16-17 and mayalso include at least a portion of the subject matter of any otheraspect or aspects disclosed herein, prior to electromagnetically formingfirst end 131 a of torque tube 130 (block 910), a perimeter length offirst virtual cross-section 118 of outer coupling surface 114 of tubeengagement portion 112 of first end fitting 110 a is substantially equalto an inner perimeter length of a cross-section of torque tube 130. Forpurposes of this disclosure, the term “substantially equal” refer to thedifference between the perimeter length of outer coupling surface 114 offirst virtual cross-section 118 (see, e.g., FIG. 5) and the innerperimeter length of a cross-section of torque tube 130 being less than1% or even less than 0.5%. If the perimeter length of inner couplingsurface 134 is much greater than the inner perimeter length of across-section of torque tube 130, then inner coupling surface 134 mayformed over outer coupling surface 114 may have wrinkles. On the otherhand, if the length of inner coupling surface 134 is much smaller thanthe inner perimeter length of a cross-section of torque tube 130, thenthe walls of torque tube 130 in end fitting engagement portion 132 maybe excessively stretched, which may result in loss of mechanicalintegrity. It should be noted that after electromagnetic forming 910,inner coupling surface 134 and outer coupling surface 114 coincide,therefore, at this stage, the perimeter length of inner coupling surface134 matches the perimeter length of outer coupling surface 114. Overall,changes in the length of inner coupling surface 134 duringelectromagnetic forming 910 are undesirable and should be minimized.

Referring e.g. to FIGS. 1, 3A-3B, and 4A-4B, in aspect 19 of the presentdisclosure, which includes at least a portion of the subject matter ofany of aspects 16-18 and may also include at least a portion of thesubject matter of any other aspect or aspects disclosed herein, outercoupling surface 114 of tube engagement portion 112 of first end fitting110 a comprises at least one first concavity 124 and at least one firstconvexity 126. All contours of outer coupling surface 114 are smooth.Outer coupling surface 114 of tube engagement portion 112 is shown inFIGS. 3A-3B and 4A-4B. Specifically, first concavity 124 and firstconvexity 126 are shown in two different sectional views, i.e., as apart of first virtual cross-section 118 in FIGS. 3A-3B and as a part offirst virtual longitudinal section 121 in FIGS. 4A-4B. In both of thesefigures, first concavity 124 and first convexity 126 are represented bysmooth curves that do not have any corner vertices. This aspect isdescribed above with respect to first virtual tangent lines 120 andfourth virtual tangent lines 123. Furthermore, this aspect demonstrates,at least in part, that all contours of outer coupling surface 114 aresmooth.

Referring e.g. to FIGS. 1, 7A, 7B, 8, and 9, in aspect 20 of the presentdisclosure, which includes at least a portion of the subject matter ofaspect 19 and may also include at least a portion of the subject matterof any other aspect or aspects disclosed herein, afterelectromagnetically forming first end 131 a of torque tube 130 (FIG. 9,block 910), inner coupling surface 134 of end fitting engagement portion132 of first end 131 a of torque tube 130 comprises at least one secondconvexity 174 complementary to at least one first concavity 124. Innercoupling surface 134 also comprises at least one second concavity 170complementary to at least one first convexity 126. All contours of innercoupling surface 134 are smooth. Inner coupling surface 134 of torquetube 130 is shown in FIGS. 7 and 8. Specifically, second concavity 170and second convexity 174 are shown in two different sectional views,i.e., as a part of first virtual cross-section 138 in FIG. 7 and as apart of second virtual longitudinal section 144 in FIG. 8. In both ofthese figures, second concavity 170 and second convexity 174 arerepresented by smooth curves that do not have any corner vertices. Thisaspect is described above with respect to second virtual tangent lines143 and fifth virtual tangent lines 146. Furthermore, this aspectdemonstrates, at least in part, that all contours of inner couplingsurface 134 are smooth.

Referring e.g. to FIGS. 1, 6A-6B, 7A-7B, and 9, in aspect 21 of thepresent disclosure, which includes at least a portion of the subjectmatter of any of aspects 16-20 and may also include at least a portionof the subject matter of any other aspect aspects disclosed herein,after electromagnetically forming first end 131 a of torque tube 130(block 910), outer surface 154 of end fitting engagement portion 132 offirst end 131 a of torque tube 130 comprises at least one thirdconcavity 180 and at least one third convexity 184. All contours ofouter surface 154 are smooth. Outer surface 154 of torque tube 130 isshown in FIGS. 7A, 7B, and 8. Specifically, third concavity 180 andthird convexity 184 are shown in two different sectional views, i.e., asa part of third virtual cross-section 156 in FIGS. 7A and 7B and as apart of third virtual longitudinal section 162 in FIG. 8. In both ofthese figures, third concavity 180 and third convexity 184 arerepresented by smooth curves that do not have any corner vertices. Thisaspect is described above with respect to third virtual tangent lines160 and sixth virtual tangent lines 166. Furthermore, this aspectdemonstrates, at least in part, that all contours of outer surface 154are smooth.

Examples of the present disclosure may be described in the context ofaircraft manufacturing and service method 1500 as shown in FIG. 15 andaircraft 1602 as shown in FIG. 16. During pre-production, illustrativemethod 1500 may include specification and design (block 1504) ofaircraft 1502 and material procurement (block 1506). During production,component and subassembly manufacturing (block 1508) and systemintegration (block 1510) of aircraft 1502 take place. Thereafter,aircraft 1502 may go through certification and delivery (block 1512) tobe placed in service (block 1514). While in service by a customer,aircraft 1502 may be scheduled for routine maintenance and service(block 1516). Routine maintenance and service may also includemodification, reconfiguration, refurbishment, etc. of one or moresystems of aircraft 1502.

Each of the processes of illustrative method 1100 may be performed orcarried out by a system integrator, a third party, and/or an operator(e.g., a customer). For the purposes of this description, a systemintegrator may include, without limitation, any number of aircraftmanufacturers and major-system subcontractors; a third party mayinclude, without limitation, any number of vendors, subcontractors, andsuppliers; and an operator may be an airline, leasing company, militaryentity, service organization, and so on.

As shown in FIG. 16, aircraft 1602 produced by illustrative method 1600may include airframe 1618 with a plurality of high-level systems 1620and interior 1622. Examples of high-level systems 1620 include one ormore of propulsion system 1624, electrical system 1626, hydraulic system1628, and environmental system 1630. Any number of other systems may beincluded. Although an aerospace example is shown, the principlesdisclosed herein may be applied to other industries, such as theautomotive industry. Accordingly, in addition to aircraft 1602, theprinciples disclosed herein may apply to other vehicles, e.g., landvehicles, marine vehicles, space vehicles, etc.

Apparatus and methods shown or described herein may be employed duringany one or more of the stages of the manufacturing and service method1500. For example, components or subassemblies corresponding tocomponent and subassembly manufacturing (block 1508) may be fabricatedor manufactured in a manner similar to components or subassembliesproduced while aircraft 1602 is in service. Also, one or more aspects ofthe apparatus, method, or combination thereof may be utilized duringproduction stages (blocks 1508 and 1510), for example, by substantiallyexpediting assembly of or reducing the cost of aircraft 1602. Similarly,one or more aspects of the apparatus or method realizations, or acombination thereof, may be utilized, for example and withoutlimitation, while aircraft 1602 is in service, e.g., maintenance andservice stage (block 1616).

Different aspects and examples of the apparatus and methods disclosedherein include a variety of components, features, and functionalities.It should be understood that the various aspects and examples of theapparatus(es) and method(s) disclosed herein may include any of thecomponents, features, and functionalities of any of the other aspectsand examples of the apparatus(es) and method(s) disclosed herein in anycombination, and all of such possibilities are intended to be within thespirit and scope of the present disclosure.

Many modifications of aspects and examples set forth herein will come tomind to one skilled in the art to which the present disclosure pertainshaving the benefit of the teachings presented in the foregoingdescriptions and the associated drawings.

Therefore, it is to be understood that the present disclosure is not tobe limited to the specific aspects and examples presented and thatmodifications and other aspects and examples are intended to be includedwithin the scope of the appended claims. Moreover, although theforegoing description and the associated drawings describe aspects andexamples of the present disclosure in the context of certainillustrative combinations of elements and/or functions, it should beappreciated that different combinations of elements and/or functions maybe provided by alternative implementations without departing from thescope of the appended claims.

What is claimed is:
 1. An apparatus (100), comprising a first endfitting (110 a) that comprises a tube engagement portion (112) andwherein: the tube engagement portion (112) comprises an outer couplingsurface (114); the outer coupling surface (114) has a first virtualcross-section (118); the first virtual cross-section (118) comprises afirst transverse inflection point (119); and each point along the firstvirtual cross-section (118) has a first virtual tangent line (120),coplanar with the first virtual cross-section (118).
 2. The apparatus(100) as in claim 1, further comprising a torque tube (130), coupled tothe first end fitting (110 a) and wherein: the torque tube (130)comprises an end fitting engagement portion (132), conformed to the tubeengagement portion (112) of the first end fitting (110 a); the endfitting engagement portion (132) comprises an inner coupling surface(134); the inner coupling surface (134) has a second virtualcross-section (138), coplanar with and complementary to the firstvirtual cross-section (118); the second virtual cross-section (138)comprises a second transverse inflection point (142); and each pointalong the second virtual cross-section (138) has a second virtualtangent line (143) coplanar with the second virtual cross-section (138).3. The apparatus (100) as in claim 2, wherein: the end fittingengagement portion (132) further comprises an outer surface (154); theouter surface (154) has a third virtual cross-section (156), coplanarwith the second virtual cross-section (138); the third virtualcross-section (156) comprises a third transverse inflection point (158);and each point along the third virtual cross-section (156) has a thirdvirtual tangent line (160), coplanar with the third virtualcross-section (156).
 4. The apparatus (100) as in claim 2, wherein thetorque tube (130) comprises titanium.
 5. The apparatus (100) as in claim2, wherein the torque tube (130) has a wall thickness between about 0.04and about 0.06 inches.
 6. The apparatus (100) as in claim 1, wherein:the first end fitting (110 a) further comprises a connector portion(111), adjacent the tube engagement portion (112), and the connectorportion (111) comprises means (113) for connecting the apparatus (100)to one of a drive unit or a driven unit.
 7. The apparatus (100) as inclaim 1, wherein: the outer coupling surface (114) of the tubeengagement portion (112) comprises a first virtual longitudinal section(121); the first virtual longitudinal section (121) comprises a firstlongitudinal inflection point (122); and each point along the firstvirtual longitudinal section (121) has a fourth virtual tangent line(123), coplanar with the first virtual longitudinal section (121). 8.The apparatus (100) as in claim 7, further comprising a torque tube(130), coupled to the first end fitting (110 a) and wherein: the torquetube (130) comprises an end fitting engagement portion (132), conformedto the tube engagement portion (112) of the first end fitting (110 a);the end fitting engagement portion (132) comprises an inner couplingsurface (134); the inner coupling surface (134) has a second virtuallongitudinal section (144), coplanar with and complementary to the firstvirtual longitudinal section (121); the second virtual longitudinalsection (144) comprises a second longitudinal inflection point (145);and each point along the second virtual longitudinal section (144) has afifth virtual tangent line (146) coplanar with the second virtuallongitudinal section (144).
 9. The apparatus (100) as in claim 8,wherein: the end fitting engagement portion (132) further comprises anouter surface (154); the outer surface (154) comprises a third virtuallongitudinal section (162), coplanar with the second virtuallongitudinal section (144); the third virtual longitudinal section (162)comprises a third longitudinal inflection point (164); and each pointalong the third virtual longitudinal section (162) has a sixth virtualtangent line (166), coplanar with the third virtual longitudinal section(162).
 10. A vehicle (104) comprising: an apparatus (100) comprising: afirst end fitting (110 a), comprising a tube engagement portion (112),wherein: the tube engagement portion (112) comprises an outer couplingsurface (114), all contours of the outer coupling surface (114) aresmooth, and the outer coupling surface (114) comprises at least onefirst concavity (124) and at least one first convexity (126); a secondend fitting (110 b); and a torque tube (130), comprising a first end(131 a) and a second end (131 b); and wherein: the first end (131 a) ofthe torque tube (130) is coupled to the first end fitting (110 a); thesecond end (131 b) of the torque tube (130) is coupled to the second endfitting; the first end (131 a) of the torque tube (130) comprises an endfitting engagement portion (132); the end fitting engagement portion(132) comprises an inner coupling surface (134) conformed to the outercoupling surface (114) of the tube engagement portion (112) of the firstend fitting (110 a); all contours of the inner coupling surface (134)are smooth, the inner coupling surface (134) comprises at least onesecond convexity (174), complementary to the at least one firstconcavity (124) of the outer coupling surface (114) of the tubeengagement portion (112), and the inner coupling surface (134) comprisesat least one second concavity (170), complementary to the at least onefirst convexity (126) of the outer coupling surface (114) of the tubeengagement portion (112); a drive unit (102), coupled to the first endfitting (110 a); and a driven unit (103), coupled to the second endfitting.
 11. The vehicle (104) as in claim 10, wherein: the end fittingengagement portion (132) of the torque tube (130) further comprises anouter surface (154); the outer surface (154) comprises at least onethird concavity (180) and at least one third convexity (184); and allcontours of the outer surface (154) are smooth.
 12. The vehicle (104) asin claim 11, wherein the outer surface (154) of the end fittingengagement portion (132) of the torque tube (130) further comprises atleast one third flat (182).
 13. The vehicle (104) as in claim 11,wherein the at least one third concavity (180) comprises a smallestradius of curvature of between 0.125 and 0.25 inches.
 14. The vehicle(104) as in claim 10, wherein the outer coupling surface (114) furthercomprises at least one first flat (125).
 15. The vehicle (104) as inclaim 14, wherein: the inner coupling surface (134) further comprises atleast one second flat (172); and the at least one second flat (172) iscomplementary to the at least one first flat (125).
 16. The vehicle(104) as in claim 14, wherein: the inner coupling surface (134) furthercomprises at least one second flat (172); and each of the at least onesecond flat (172) is complementary to a different one of the at leastone first flat (125).
 17. The vehicle (104) as in claim 10, wherein theinner coupling surface (134) further comprises at least one second flat(172).
 18. The vehicle (104) as in claim 17, wherein the at least onesecond flat (172) is located between the at least one second convexity(174) and the at least one second concavity (170).
 19. The vehicle (104)as in claim 17, wherein one of the at least one second flat (172) islocated between two of the at least one second convexity (174).
 20. Thevehicle (104) as in claim 17, wherein one of the at least one secondflat (172) is located between two of the at least one second concavity(170).